Hi Brett,
First thing to do is go through and retrace your steps. Go through the whole screen replacement procedure again and in the process check all of the connectors you unplug. Get yourself a magnifying glass and a nice bright light and check the cables for any kind of tear or damage, then examine the FPC connectors on both sides (cable and logic board) for any bent or missing pins. Bent pins can sometimes be straightened with some fine tip tweezers, but broken or missing pins will require the connector to be replaced. Check around the connector on the logic board for any small components that may have gotten knocked off in the process of connecting and disconnecting those plugs.
If everything looks okay, clean all of the connectors with 90% or higher concentration isopropyl (rubbing) alcohol, let them dry and reassemble and reevaluate.
Typically the screen doesn't usually cause boot loops; usually you'll see either no display or no touch screen function. However, the earpiece speaker assembly mounted on the screen is very susceptible to damage and can cause boot loops, so you might try unplugging that connector and seeing if the phone will boot then.
Give that a try then come on back and let us know what you find and what happens and we'll try to figure out what to do next based on your results.